A B is a vertical tower. The point A is on the ground and C is the middle point of A B . The part C B subtend an angle α at a point P on the ground. If A P = n A B , then the correct relation is

Step-by-step solution

In ∆ P A B , tan ⁡ β = A B A P In ∆ P A C , tan ⁡ θ = A C A P ∴ tan ⁡ α = tan ⁡ β - θ = tan ⁡ β - tan ⁡ θ 1 + tan ⁡ β tan ⁡ θ = A B A P - A C A P 1 + A B A P ⋅ A C A P ...(i) ∵ A P = n A B = n 2 A C ( ∵ C is the mid point of B A ) From Eq. (i), we get tan ⁡ α = 1 n - 1 2 n 1 + 1 2 n 2 = n 2 n 2 + 1 ⇒ n = 2 n 2 + 1 tan ⁡ α